Analysis of Harrington limit for electrically small antenna directivity

Harrington has demonstrated a relation which links antenna directivity and size. This relationship has been calculated considering lossless antennas and represents the antenna directivity limit. In the case of electrically small antennas, this limit does not respect the directivity definition with a negative value (dB, maximum D <; 1 in linear scale) when 2r/A <; 0.13 and does not converges to the directivity of the infinitesimal Huygens source. In this paper, a renormalization of the Harrington limit is proposed to fulfill both directivity definition and physical behavior in the case of electrically small antennas.